The enthusiasm with which U.S. troops are being greeted in the Kurdish north is real. But in the rest of the country, especially in the capital, it is a potentially dangerous mirage.

Greeting enemy conquerors with cheers is an old Arab custom. The Lebanese villagers who welcomed invading Israeli troops with rice and roses in June 1982 were heaving grenades at them by the end of the year.

True, the citizens of Baghdad are happy to see the Iraqi dictator go. But his fall also presents them with a narrative problem.

For more than 30 years, the great majority of Iraqis supported - or, at the very least, passively acquiesced to - an evil regime. As they betrayed their friends and families, they told themselves they had no choice - Saddam was too fearsome to resist. But the American invasion has exposed the truth: The Butcher of Baghdad was nothing more than a hollow buffoon. Which poses an awkward question: What does that make the millions who feared and followed him?

The Arab Middle East deals with awkward questions by producing face-saving lies, and already a cover story is emerging. Everyone hated Saddam all along. No one collaborated with him. Topple his statue, beat his picture with a shoe, denounce him to cameramen, and a great society will be restored to its former glory.

This alibi ignores the fact that a vast number of Iraqis belonged to Saddam's party. It also fails to account for the fact that even before Saddam, Iraq was a brutish and backward nation, a place ruled by repression, sectarian pogroms and political violence.

Iraq's founding Hashemite monarchy was a primitive desert tyranny that in 1940 tried to make an alliance with Hitler. When it was overthrown by a junta in 1958, Col. Abdel Karim Kassem hanged the king's men from Baghdad lampposts. Crowds cheered then, too. And they cheered again five years later, when Kassem was machine-gunned to death by Baath Party hit men.

The looters loose on the streets of Baghdad today are there for a variety of reasons. Some want revenge. Some want free furniture. Some want to let off steam. Some want to impress their new American masters.

But rioting usually contains a large element of self-hatred. The mobs would like to burn and sack their way out of their complicity in decades of evil. But purification isn't bought so easily. The mob knows the truth about who over the decades has done what to whom.

Beyond Iraq, too, Arabs are grappling for a narrative that can explain their situation. As usual, the default position is to blame the Jews. On Thursday, the Arab News, an English-language mouthpiece for the Saudi government, lamented that Iraq is now "vulnerable to exploitation by the conservative Zionist junta who have taken over the White House." Meanwhile, Arab League head Amr Musa raced to the UN to inform Secretary General Kofi Annan that the only way out of the present crisis is to force Israel to make concessions.

If the U.S. hopes to build a decent government in Iraq - and eventually beyond - it can't do it on lies. The Iraqis don't love America. They don't even love themselves.

But if the U.S. plays it straight and refuses to buy the self-serving delusions being peddled on the streets of Baghdad and in other Arab capitals, it can elicit something more important than love - cooperation. For that, it will need a military administration, temporary to be sure, that is long on Gen. Douglas MacArthur and very short on Sally Field.

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